Years ago, Dr. Issac Asimov was such a wonderful writer that he could explain anything so that it made perfect sense. Slide-rules, cholesterol, neutrinos, all were gist for his typewriter. In one memorable essay, "Music to my ears" he explained the design of the major scale so well that I still remember the principles 40 years after reading it. This posting is dedicated to the good doctor.
The tonic and the upper tonic, plucked together sound smooth & consonant, yet different . Further, plucking just one makes the other string vibrate, unless muted by a finger, courtesy of the vibrations transmitted through the soundboard. You suddenly have variety: the number of possible sounds has leapt. From a toy, an instrument has emerged.
And relativity still reigns. If there is above the tonic a note that is dominant to it, there must be a note below the tonic such that the tonic is dominant to. Call this the Subdominant. It lives up to it's name, sounding and feeling somewhat over-topped by the tonic. It is exactly is 2/3 the pitch of the tonic (2/3 * 3/2 = 1).
Filling in the dominant of the lower-Tonic (3/4 of the Tonic), and the sub-dominant of the upper-Tonic (4/3 of the Tonic). This makes for a nice little instrument, with no real dissonances and plenty of strings to pluck, mute or leave open. These three notes are still the foundation notes used by bass players everywhere.
The gap between the sub dominant and dominant notes all have a natural spacing that seems about right, so call it a Wholetone.
Musical Technology marches on.
In particular, halfway between the tonic and the Dominant is a spot just 5/4 higher than the tonic that sounds special. Since it is about midway between the tonic and the dominant, you call it the Mediant. -
Is there a Sub-Mediant? Of course(!), at the 4/5 point below the Tonic, perhaps a bit harder to discern.
However, there a big gap between the tonic and the mediant. Fortunately there's another note you can add to fill it; the dominant of the dominant, this gives you a note between the tonic and the mediant, just above the tonic, the super-tonic. This gives you 3 sets of 3-note chords with a tonic-mediant-dominant structure, such a cool-sounding and useful chord that you call it the major chord. -
There are also three chords with a sub-mediant in them. These later chords have a different sound than the major chords, their sub-mediant note is buried under the Dominant and pushing a bit close to the Tonic, so sounds tight or restricted, so you naturally call them the Minor chords.
There's just one more note to name, the note just under the Tonic. Somehow, despite being created by playing only progressive sequences of notes it somehow has an implied dissonance against the tonic and the listener's ear knows it, even when the tonic is not playing. But this creates a cool musical tension that can make the music interesting. It creates notes that want to be "led back" to the tonic, creating a resolution. So call it the Leading Tone.-
This is instrument enough for several centuries of development of fine music. Enough time so that the notes are given a second set of names: that correspond to the number that they are from the tonic, in roman numerals; Arabic numerals and the concept of zero are still in the future:
I Tonic UnityII Super-Tonic SecondIII Mediant ThirdIV Sub-Dominant FourthV Dominant FifthVI Sub-Mediant SixthVII Leading Tone SeventhVIII (upper-)Tonic Octave
What about going the other way, going from the Sub-dominant to it's subdominant? This gives you a note a fourth below the Fourth that does not have a name (with one exception none of these fancy new notes has a name) called the Minor Seventh , halfway between the normal "major" Sixth and "major" Seventh. Again this note makes a whole pile of sense in some arrangements. Again, once this game starts you quickly fill in all the notes down to the octave below. and, of course, this gets called the Circle of Fourths.
Every keyboard needs more Mediants
This kind of simple musical arrangement using dominants was all the rage in the 8th and 9th centuries (a good link to Gregorian chant is wanted here, any suggestions?). But over time instruments improved in clarity and arrangers learned how to incorporate the mediant or third, into chords. But there's a wonderful ambiguity about thirds: should they be a major third above the root, or a major third below the Dominant? In the major scale some chords have mediants, the major third, and some are minor chords with a sub-mediant, a minor third in them. In the early days one could imagine a musician deftly retuning his or her instrument's thirds to suit the next song, but as the instruments grew heavier and more strings were added, this became a challenge.
So musician naturally wanted keys added the keyboards, so that every note had a mediant and a submediant.
Invasion of the "accidentals"
Musicial naming theory is an incredibly hoary and old thing. the black notes on the piano were added over 800 years ago, yet still have no real names, only relative names like Minor this or Augmented that, and are called accidentals.
More to come.
One day I'll write about the Tuning wars: "Just tuning" purists vs the "good enough" pragmatists.